Answer:
Correct choice is C: 52 square units
Step-by-step explanation:
Rectangle ABCD has vertices at points A(-1,6), B(4,5), C(2,-5) and D(-3,-4). The segment AB is rectangle width and the segment BC is rectangle length. Then
[tex]AB=\sqrt{(-1-4)^2+(6-5)^2}=\sqrt{(-5)^2+1^2}=\sqrt{25+1}=\sqrt{26}\ un.,\\ \\BC=\sqrt{(2-4)^2+(-5-5)^2}=\sqrt{(-2)^2+(-10)^2}=\sqrt{4+100}=\sqrt{104}=2\sqrt{26}\ un.[/tex]
Then the areq of the rectangle is
[tex]A=AB\cdot BC=\sqrt{26}\cdot 2\sqrt{26}=2\sqrt{26\cdot 26}=2\cdot 26=52\ un^2.[/tex]
